Generic coarse geometry of leaves:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham
Springer
[2018]
|
| Series: | Lecture notes in mathematics
2223 |
| Subjects: | |
| Online Access: | Inhaltstext http://www.springer.com/ Inhaltsverzeichnis |
| Physical Description: | xv, 171 Seiten 23.5 cm x 15.5 cm |
| ISBN: | 9783319941318 3319941313 |
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MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Introduction 1
Part I Coarse Geometry of Metric Spaces
2 Coarse Quasi-Isometries 13
2 1 Notation, Conventions and Terminology 13
2 2 Coarse Quasi-Isometries 14
2 3 Coarse Composites 16
24A Coarsely Quasi-Isometric Version
of Arzela-Ascoli Theorem 19
2 5 Large Scale Lipschitz Maps 19
2 6 Coarse and Rough Maps 24
3 Some Classes of Metric Spaces 29
3 1 Graphs 29
3 2 Metric Spaces of Coarse Bounded Geometry 32
3 3 Coarsely Quasi-Symmetric Metric Spaces 34
3 4 Coarsely Quasi-Convex Metric Spaces 35
4 Growth of Metric Spaces 37
4 1 Growth of Non-decreasing Functions 37
4 2 Growth of Metric Spaces 38
4 3 Growth Symmetry 41
5 Amenability of Metric Spaces 43
5 1 Amenability 43
5 2 Amenable Symmetry 47
6 Coarse Ends 51
6 1 Ends 51
6 2 Coarse Connectivity 52
6 3 Coarse Ends 54
xiii
XIV
Contents
6 4 Functoriality of the Space of Coarse Ends 58
6 5 Coarse End Space of a Class of Metric Spaces 61
7 Higson Corona and Asymptotic Dimension 65
7 1 Compactifications 65
7 2 Higson Compactification 68
7 3 Asymptotic Dimension 73
Part II Coarse Geometry of Orbits and Leaves
8 Pseudogroups 77
8 1 Pseudogroups 77
8 2 Coarse Quasi-Isometry Type of Orbits 79
83A Coarse Version of Local Reeb Stability 81
8 4 Topological Dynamics 85
841 Preliminaries on Baire Category 85
842 Saturated Sets 86
843 The Property of Being Recurrent on Baire Sets 87
844 Pseudogroups Versus Group Actions 88
9 Generic Coarse Geometry of Orbits 91
9 1 Coarsely Quasi-Isometric Orbits 92
9 2 Growth of the Orbits 95
921 Orbits with the Same Growth Type 95
922 Some Growth Classes of the Orbits 97
9 3 Amenable Orbits 102
9 4 Asymptotic Dimension of the Orbits 105
9 5 Highson Corona of the Orbits 108
951 Limit Sets 108
952 Semi Weak Homogeneity of the Higson Corona 112
9 6 Measure Theoretic Versions 113
10 Generic Coarse Geometry of Leaves 115
10 1 Foliated Spaces 115
10 2 Saturated Sets 118
10 3 Coarse Quasi-Isometry Type of the Leaves 119
10 4 Higson Corona of the Leaves 124
10 4 1 Higson Compactification 124
10 4 2 Limit Sets 125
10 5 Algebraic Asymptotic Invariants 127
10 6 Versions with Quasi-Invariant Currents 129
10 7 There Is No Measure Theoretic Version of Recurrence 131
11 Examples and Open Problems 133
11 1 Foliated Spaces Defined by Suspensions 133
11 2 Foliated Spaces Defined by Locally Free Actions
ofLieGroups 134
Contents
xv
11 3 Inverse Limits of Covering Spaces 135
11 4 Bounded Geometry and Leaves 135
11 5 Graph Spaces 138
11 6 Case of Cayley Graphs 140
11 7 Construction of Limit-Aperiodic Functions 142
11 8 Graph Matchbox Manifolds 143
11 9 Concrete Examples of Graph Matchbox Manifolds 145
11 9 1 The Ghys-Kenyon Matchbox Manifold 145
11 9 2 An Example with Uncountably Many Growth
Types of Leaves 148
11 9 3 An Example with Equi-Amenable Dense Leaves
and Other Non-amenable Leaves 149
11 9 4 An Example with Leaves of Infinite Asymptotic
Dimension 150
11 10 Foliations of Codimension One 150
11 10 1 Hector’s Example 151
11 10 2 Generic Ergodicity of Equivalence Relations 153
11 10 3 Generic Ergodicity of Metric Equivalence
Relations 154
11 10 4 Generic Ergodicity of the Growth Type Relation
in Hector’s Example 155
11 10 5 The Theory of Levels 159
11 11 Open Problems 161
References 163
Index
|
| any_adam_object | 1 |
| author | Alvarez López, Jesús A. Candel, Alberto 1961- |
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| author_role | aut aut |
| author_sort | Alvarez López, Jesús A. |
| author_variant | l j a a lja ljaa a c ac |
| building | Verbundindex |
| bvnumber | BV045146882 |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)1048618220 (DE-599)DNB1159583625 |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:09:58Z |
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| institution_GND | (DE-588)1064344704 |
| isbn | 9783319941318 3319941313 |
| language | English |
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| publishDate | 2018 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Alvarez López, Jesús A. (DE-588)1089688431 aut Generic coarse geometry of leaves Jesús A. Álvarez López, Alberto Candel Cham Springer [2018] © 2018 xv, 171 Seiten 23.5 cm x 15.5 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2223 Riemannsche Blätterung (DE-588)4195597-3 gnd rswk-swf Asymptotic Dimension Coarse Quasi-isometry Foliated Space Growth Leaf Riemannsche Blätterung (DE-588)4195597-3 s DE-604 Candel, Alberto 1961- (DE-588)173386210 aut Springer International Publishing (DE-588)1064344704 pbl Erscheint auch als Online-Ausgabe 978-3-319-94132-5 Lecture notes in mathematics 2223 (DE-604)BV000676446 2223 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=23ce89517b144f06bce1a87adfff9351&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.springer.com/ HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030536605&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alvarez López, Jesús A. Candel, Alberto 1961- Generic coarse geometry of leaves Lecture notes in mathematics Riemannsche Blätterung (DE-588)4195597-3 gnd |
| subject_GND | (DE-588)4195597-3 |
| title | Generic coarse geometry of leaves |
| title_auth | Generic coarse geometry of leaves |
| title_exact_search | Generic coarse geometry of leaves |
| title_full | Generic coarse geometry of leaves Jesús A. Álvarez López, Alberto Candel |
| title_fullStr | Generic coarse geometry of leaves Jesús A. Álvarez López, Alberto Candel |
| title_full_unstemmed | Generic coarse geometry of leaves Jesús A. Álvarez López, Alberto Candel |
| title_short | Generic coarse geometry of leaves |
| title_sort | generic coarse geometry of leaves |
| topic | Riemannsche Blätterung (DE-588)4195597-3 gnd |
| topic_facet | Riemannsche Blätterung |
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